What is (\partial)/(\partial x)(x^8+8xy^7) ?

The answer to (\partial)/(\partial x)(x^8+8xy^7) is 8x^7+8y^7

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(\partial)/(\partial x)(x^8+8xy^7)

\frac{\partial}{\partial x} (x^{8} + 8 x y^{7})

8 x^{7} + 8 y^{7}

Solution steps

\frac{\partial}{\partial x} (x^{8} + 8 x y^{7})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{8}) + \frac{\partial}{\partial x} (8 x y^{7})

\frac{\partial}{\partial x} (x^{8}) = 8 x^{7}

\frac{\partial}{\partial x} (8 x y^{7}) = 8 y^{7}

= 8 x^{7} + 8 y^{7}

\int 1 d x^{3}

f (x) = \frac{x ^{2}}{ln ( x )}

\frac{d}{d x} (2 x^{2} - 6 x)

\int 4 x^{- 1} d x

\frac{\partial}{\partial x} (e^{6 x y})

What is (\partial)/(\partial x)(x^8+8xy^7) ?
The answer to (\partial)/(\partial x)(x^8+8xy^7) is 8x^7+8y^7